Where can I find the correct invisible zipper foot and shank for my Singer 5062C?

go to a pfaff shop or any sewing machine repair shop and get a 1/2 foot for zippers

If you can buy an adapter shank for your machine, you can then purchase a generic snap-on zipper foot.
Sewing machine feet Super high shank high shank slant shank low shank snap...

This is posted in the UK, but you should be able to find something similar in the US:
Toyota 2260 Sewing Machine Feet Bobbins Needles Parts

Stitchery Sewing Machine Attachments Needle and Thread

http://www.sewingpartsonline.com/sewing-machine-presser-feet.aspx

Presser Feet Snap on and Screw on for Sewing Embroidery and Serger Machines

...

here is a link for parts for the machine

here are some link to check out
http://www.sewingpartsonline.com/singer-6136-sewing-machine-parts.aspx
http://www.sewingpartsonline.com/zipper-foot-singer-507836.aspx

http://www.sewingpartsonline.com/zipper-presser-foot-low-shank-55411.aspx

http://www.sewingpartsonline.com/snap-on-presser-feet-set-low-shank-11-piece.aspx
also try ebay for parts

Have you got the right zip foot for the machine ? there are two types short shank and large shank unless you have a snap on foot, if all the other feet touch the fabric then you definitely have the wrong foot

Are you making sure the little metal bar is lined up with the little snap on grip?

hi Joanne.
this is all i could find out from the internet hope it helps you out.
Directions for attaching using the zipper foot for Singer model Google...
go to this link.

I would suggest that you try http://www.sewingpartsonline.com/zig-zag-foot-standard-low-shank.aspx the page shows this foot as being suitable for your machine.

Many low shank sewing machine feet are interchangeable.

a generic low shank Zipper foot is also there http://www.sewingpartsonline.com/zipper-presser-foot-low-shank-55411.aspx

Trust that this helps you.

My invisible zipper foot is a plastic generic one which was describd as being "low shank" and it works fine on three different Elnas I own.

I would have thought your machine was a low shank style too, there is a fair bit of similarity between feet with low shank clip on style. So if your feet clip on and off the shank, then you should be able to clip on another type of foot too.

if you try this link http://www.sewingpartsonline.com/sewing-machine-presser-feet.aspx

then go through to the page for the foot attachment system that looks like yours you might be able to establish which one you need. THere is a brother high shank invisble foot listed, and an alternative part number. I jcan't see a Brother SC9500 machine listed so you might need to do a bit of elimination.

You could also email sewingpartsonline.com and ask them to help you identify the right foot.

www.singerco.com